Efficient probabilistic slope stability analysis using conditional probability-based weighted low-discrepancy simulation

Traditional deterministic slope stability analysis frequently neglects the influence of various uncertainties inherent in soil properties. Recently, probabilistic analysis has seen great success in slope stability analysis, however, the direct simulation of low-level failure probabilities of earth slopes still faces some computational challenges. To solve such an issue, this study presents an improved weighted low-discrepancy simulation (WLDS) method for efficient probabilistic slope stability analysis, especially for random variable model (RVM). This method incorporates a series of intermediate events into the WLDS framework, effectively transforming the calculation of failure probability into a product of relatively large conditional probabilities, which can significantly improve the computational efficiency. In accordance with probabilistic theory, the variance in the probability of generating randomized low-discrepancy samples within a specified subset is employed as a viable criterion to determine intermediate threshold values. Furthermore, to increase the likelihood of the sample generation in each intermediate event, a reduction strategy for intermediate sampling space is adopted, which can enhance the sampling efficiency to generate conditional samples. The efficiency and accuracy of the proposed method are demonstrated through one mathematical function case and three slope stability cases. In combination with probabilistic weight strategy, the multiple most probable failure points (multi-MPPs) can be easily identified, which represents different slope failure modes. Last but not least, when dealing with correlated random variables, the unique capability of the proposed method in reliability updating with no additional evaluations of performance function is discussed.